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ORIGINAL PAPER
Flow and Heat Transfer at a Nonlinearly Shrinking Porous Sheet:The Case of Asymptotically Large Powerlaw Shrinking Rates
1
Department of Mathematics, Bangalore University Bangalore 560001, INDIA
2
Department of Mathematics University of Central Florida Orlando, Florida 32816, USA
3
Faculty of Mathematics, University of Cluj R-3400 Cluj, CP 253, ROMANIA
Online publication date: 2013-09-06
Publication date: 2013-08-01
International Journal of Applied Mechanics and Engineering 2013;18(3):779-791
KEYWORDS
ABSTRACT
The boundary layer flow and heat transfer of a viscous fluid over a nonlinear permeable shrinking sheet in a thermally stratified environment is considered. The sheet is assumed to shrink in its own plane with an arbitrary power-law velocity proportional to the distance from the stagnation point. The governing differential equations are first transformed into ordinary differential equations by introducing a new similarity transformation. This is different from the transform commonly used in the literature in that it permits numerical solutions even for asymptotically large values of the power-law index, m. The coupled non-linear boundary value problem is solved numerically by an implicit finite difference scheme known as the Keller- Box method. Numerical computations are performed for a wide variety of power-law parameters (1 < m < 100,000) so as to capture the effects of the thermally stratified environment on the velocity and temperature fields. The numerical solutions are presented through a number of graphs and tables. Numerical results for the skin-friction coefficient and the Nusselt number are tabulated for various values of the pertinent parameters.
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